Over the past five weeks Greenpeace Davids in inflatable dinghies have been harassing four cargo ships loaded with nearly 15,000 tons of low-level radioactive waste from the United Kingdom, Belgium, the Netherlands, and Switzerland. It has been called the largest dumping operation of its kind.

''We will continue to make life difficult for the dumpers until they put an end to their activities,'' Greenpeace spokeswoman Mickey Kaufmann told the Monitor in a telephone interview from Amsterdam.

But even in calm seas the Greenpeace Davids will have problems: The law, it seems, is on Goliath's side.

Since 1967, nearly 100,000 tons of radioactive waste from nuclear power plants, hospitals, and research laboratories in Western Europe have been dumped in the Atlantic Ocean. Since 1972, the Paris-based Nuclear Energy Agency (NEA) has supervised the dumping at the site off the Spanish coast, issuing permits and sending observers as dictated by the so-called London Dumping Convention.

''It is all entirely aboveboard,'' an NEA official said.

Indeed, courts in the UK and the Netherlands have been quick to support the dumpers. Last week a Dutch magistrate ordered Greenpeace to stop trying to prevent the vessels from dumping or face a fine of almost $1,000.

Radioactive waste continues to pile up at an alarming rate as new nuclear power plants are built. Waste disposal sites on land remain scarce in overcrowded Western Europe.

Even so, four of the Continent's main nuclear waste producers - France, West Germany, Italy, and Sweden - agreed in 1974 to stop discharging the byproduct in the sea. They will concentrate on developing other methods of waste treatment and disposal above and below ground.

The major remaining culprits, according to environmentalists, are Belgium, the Netherlands, Switzerland, and the Britain. Belgium is especially guilty: It has failed to ratify the 1972 London Convention and still allows ships to take the waste on at its ports. Half of the waste dumped in the sea this year has been from Belgian sources, environmentalists add.

The issue could come to a head next February when delegates from 80 countries gather in London to begin reexamining the continued suitability of the underwater dump site off the Spanish coast - the only one designated for West European nuclear waste. Spanish Foreign Minister Jose Pedro Perez Llorca reportedly told environmentalists earlier this month Spain would ask to have the site moved farther out from the Iberian coast, or seek to end the dumping altogether.

Meanwhile, the Greenpeace Davids have been exercising their slingshots for the next confrontation, whenever it may come.

Last week, for only the second time in the organization's history, Greenpeace activists succeeded in boarding a ship near the dump site. Though they were arrested immediately, they did delay the dumping operation for several hours. At another recent operation, several Greenpeace activists, bobbing alongside the ship in dinghies, delayed the unloading by more than 24 hours by placing themselves under the dumping derricks.

Not to be outdone, Goliath has also been exercising - his mind.

Reports from London say that the company charged with managing a fleet of nuclear transportation vessels for British Nuclear Fuels, Ltd., has it eye on a new ship that will frustrate the Greenpeace Davids and anyone else who tries to harass it. It is much larger than the one used in recent dumps, making it more difficult to board at sea. And instead of dumping the waste over the side, it discharges the steel drums from the bottom of the hull directly into the water.